Extraction of hierarchical functional connectivity components in human brain using resting-state fMRI.

The study of hierarchy in networks of the human brain has been of significant interest among the researchers as numerous studies have pointed out towards a functional hierarchical organization of the human brain. This paper provides a novel method for the extraction of hierarchical connectivity components in the human brain using resting-state fMRI. The method builds upon prior work of Sparse Connectivity Patterns (SCPs) by introducing a hierarchy of sparse overlapping patterns. The components are estimated by deep factorization of correlation matrices generated from fMRI. The goal of the paper is to extract interpretable hierarchical patterns using correlation matrices where a low rank decomposition is formed by a linear combination of a high rank decomposition. We formulate the decomposition as a non-convex optimization problem and solve it using gradient descent algorithms with adaptive step size. We also provide a method for the warm start of the gradient descent using singular value decomposition. We demonstrate the effectiveness of the developed method on two different real-world datasets by showing that multi-scale hierarchical SCPs are reproducible between sub-samples and are more reproducible as compared to single scale patterns. We also compare our method with existing hierarchical community detection approaches. Our method also provides novel insight into the functional organization of the human brain.